Fund Project:
AA was supported in part by Croatian Science Foundation under the project IP-2014-09-2285. HB and JČ were supported by the FWF stand-alone project P25975-N25. We gratefully acknowledge the support of the bilateral grant Strange Attractors and Inverse Limit Spaces,
Österreichische Austauschdienst (OeAD) -Ministry of Science, Education and Sport of the Republic of Croatia (MZOS), project number HR 03/2014.

For a point $x$ in the inverse limit space $X$ with a single unimodal bonding map we construct, with the use of symbolic dynamics, a planar embedding such that $x$ is accessible. It follows that there are uncountably many non-equivalent planar embeddings of $X$.

Figure 5.
The planar representation of an arc in $X$ with the corresponding kneading sequence $\nu=100110010\ldots$. The ordering on basic arcs is such that the basic arc coded by $ L=1^{\infty}.$ is the largest.

Figure 6.
The planar representation of the same arc as in Figure 5 in $X$ with the corresponding kneading sequence $\nu=100110010\ldots$. The ordering on basic arcs is such that the basic arc coded by $ L=(101)^{\infty}.$ is the largest.